Abstract
This research work sets forward a new formulation of Linear Quadratic Regulator problem (LQR) applied to a Wind Energy Conversion System (WECS). A new necessary and sufficient condition of Lyapunov asymptotic stability is also established. The problem is mathematically described in form of Linear Matrix Inequalities (LMIs). The considered WECS is based on a Doubly Fed Induction Generator (DFIG). An appropriate Linear Parameter Varying (LPV) model is designed. This model stands for a realistic representation of the randomly time varying wind velocity. Stability and robustness of the controller over the admissible values of time varying parameter are investigated. The newly lifted Lyapunov condition gives less conservative conditions for LMI approach in case of parameter-dependent Lyapunov functions PDLF. The considered PDLF has the same variation dynamics as the system matrix. The intrinsic objective for our research is to offer more freedom degrees to the control problem and to improve the efficiency of the controller in case of uncertainties or parametric variations. The performances of the proposed theorems are validated to achieve active and reactive powers tracking of the WECS over the admissible range of wind speeds. The interesting features of the proposed solution are the simpler implementation and the larger robustness margin. It also has the advantage of providing a linear control to the considered nonlinear system without resorting to linearization. The LMIs implementation is performed on Yalmip Matlab toolbox. The proposed controller is verified on a Matlab Simulink emulator. This work presents an extension of the LQR control problem to LPV systems.
Highlights
In recent years, the growing global energy needs and the permanent increase in the fossil fuels costs stand for the main concerns inciting a big interest in renewable energy harvesting
One can deduce that the variable Lyapunov candidate matrix based regulator, which we obtained through a new Linear Matrix Inequalities (LMIs) formulation of the Lyapunov stability condition, gives an optimal index of the control cost
The main concern of this work was the Linear Quadratic Regulator problem (LQR) robust static state tracking control of a polytopic Linear Parameter Varying (LPV) Doubly Fed Induction Generator (DFIG) model based on an LMI approach
Summary
The growing global energy needs and the permanent increase in the fossil fuels costs stand for the main concerns inciting a big interest in renewable energy harvesting. The main advantage of these techniques is that the control law is able to ensure at the same time satisfactory tracking performances and stability of the system [9,10,11,12,13,14] Robustness of these controllers are mostly evaluated in different constant values of the varying parameters. The authors of [18,19,20,21,22,23] have proposed different LQR control schemes for the considered system These presented methods are mainly based either on a Linearized Time Invariant (LTI) model or on a small signal model of the system. Conclusion of this investigation is displayed in the last section
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Advanced Computer Science and Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
